The case was Obergefell v. Hodges, and it forced the court to address two questions:
1) Does the Fourteenth Amendment require a state to license a marriage between two people of the same sex?
2) Does the Fourteenth Amendment require a state to recognize a marriage between two people of the same sex when their marriage was lawfully licensed and performed out-of-state?
As we discussed, this provides the court the first opportunity to consider whether the 14th amendment's equal protection clause applies to sexual orientation. They have yet to consider this issue. The states - including Texas - argue that they have the right to discriminate in this matter because the states have a legitimate interest in promoting pro-creation, among other things.
Commentators inferred from the questions asked that the judges were split on whether this was an appropriate reason to do.
For additional info:
- Audio of the arguments can be found here.
- Transcript for the argument in question 1 here.
- Transcript for the argument in question 2 here.
- The Wikipedia page.
- The Dangers of a Constitutional 'Right to Dignity'.
- The Here and Now of Same-Sex Marriage.
- Same-sex marriage is back in the Supreme Court. Here's what a ruling will mean.